Question

The term that corrects for the attractive forces present in a real gas in the van der Waals equation is:
A. nb
B. $\dfrac{a{{n}^{2}}}{{{V}^{2}}}$
C. $-\dfrac{a{{n}^{2}}}{{{V}^{2}}}$
D. –nb

Answer 1

Hint: Van Der Waals equation explains the changing of two properties in case of gas molecules. They are the excluded volume of gas and attractive forces exist between gas molecules.
The excluded volume is corrected by introducing ‘b’ and introducing ‘a’ for magnitude of intermolecular forces.

Complete answer:
- The ideal gas law is as follows.
PV = nRT,
where P = Pressure of the gas
V = Volume of the gas
 n= Number of moles of the gas
R = gas constant
T = Temperature of the gas
- Vander Waals in 1873 modified the ideal gas law and introduced the properties of the real gases in the form of non-zero volume and pairwise attractive forces.
- The van der Waals equation shows the relation between different parameters is as follows.
\[(P+\dfrac{a{{n}^{2}}}{{{V}^{2}}})(V-nb)=RT\]
- In the above equation $\dfrac{a{{n}^{2}}}{{{V}^{2}}}$ represents the correction in pressure and nothing but the correction for attractive forces present.
- The ‘nb’ represents the correction in volume, it is because of the fact that volume occupied by the gas is considerable over the total volume of the gas.
- Therefore $\dfrac{a{{n}^{2}}}{{{V}^{2}}}$ is the term that corrects for the attractive forces present in a real gas in the van der Waals equation.

So, the correct option is B.

Note:
In general in ideal gas law the attractive forces between gas molecules and the volume occupied by the gas molecules are neglected. But van der Waal introduced those corrections in ideal gas law and proposed the van der Waal equation.